Columbo star Peter Falk died after suffering a cardiac arrest following a bout of pneumonia, according to his death certificate.The beloved actor passed away at the age of 83 at his Los Angeles home last month (Jun11). Newly-released papers, filed with the Los Angeles County Department of Public Health and obtained by Tmz.com, list Falk's main cause of death as cardiorespiratory arrest. Pneumonia is listed as an underlying cause of death, as is advanced Alzheimer's disease, which Falk had been battling towards the end of his life.